Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints

Presentation Transcript

A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1

1Instituto Superior Técnico, Lisbon, Portugal

2Tampere University of Technology, Tampere, Finland

Introduction

Efficient algorithms for multiple vehicle path planning are crucial for cooperative control systems
Need to take into account vehicle dynamics, mission parameters and external influences
Example: Go-To-Formation maneouvre

Andreas J. Häusler - IAV 2010

The Go-To-Formation Maneouvre

Current

Mother Ship

An initial formation pattern must be established before mission start
Deploying the vehicles cannot be done in formation (no hovering capabilities)
Vehicles can’t be driven to target positions separately (no hovering capabilities)

The Go-To-Formation Maneouvre

Mother Ship

Need to drive the vehicles to the initial formation in a concerted manner
Ensure simultaneous arrival times and equal speeds
Establish collision avoidance through maintaining a spatial clearance

Path Planning Foundations

Final position

Initial position

Polynomial Path Planning

Dispense with absolute time in planning a path (Yakimenko)
Establish timing laws describing the evolution of nominal speed with
Spatial and temporal constraints are thereby decoupled and captured by &
Choose and as polynomials
Path shape changes with only varying

Polynomial Path Planning

Polynomial for each coordinate with degree determined by the number of boundary conditions
Temporal speed and acceleration constraints
Choice for timing law with

CostFunctionConsiderations

Cost Function Considerations

A path is feasible if it can be tracked by a vehicle without exceeding , , and
It can be obtained by minimizing the energy consumption
subject to temporal speed and acceleration constraints

Multiple Vehicle Path Planning

Instead of trying to minimize the arrival time interval, we can fix arrival times to be exactly equal and still get different path shapes
Integrate for

Multiple Vehicle Path Planning

Then we obtain , from which the spatial paths are computed
The result is in turn used to compute velocity and acceleration
Optimization is done using direct search

Spatial Deconfliction

Final positions

(target formation)

Initial positions

Temporal Deconfliction

Final positions

(target formation)

Initial positions

Deconfliction

Spatial deconfliction: subject to
For temporal deconfliction, the constraint changes to
Simultaneous arrival at time

Environmental Constraints

Incorporated throughbarrier function
Path planningwithcurrentsformoreenergy-efficientpaths (insteadofsolelyrelying on pathfollowingcontroller)
Path planningwithcommunicationconstraintsforrangekeepingwithinthegroup

(Hauser, CDC 2006)

Path Planning System

MissionSpecifications

SpatialClearance

Optimization Algorithm

Comm. Constraint

CostCriterion

PathGeneration

InitialGuess

AMV

Data

Init. Position & Heading

Path

Nominal Paths

InitialVelocity

Time-CoordinatedPathFollowing

Final Position & Heading

Revised Guess

SpeedProfiles

Final Velocity

DynamicalConstraints

EnvironmentalConstraints

Current

Obstacles

Time-Coordinated Path Following

Closed-form solution to problems of open-loop path planning and trajectory tracking
Using virtual time with

(Ghabcheloo, ACC 2009)

Time-Coordinated Path Following

Path followingcontrolstrategy
Guaranteesthatvehiclesandaredeconflictedandthattheyfollowtheirtrajectoryif
A time coordinationcontrollawcanbefound so thatthemissionremains “near optimal“ in thepresenceofdisturbances

Simulation Results

Algorithm makes use of currents to minimize expected energy usage
Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax

Simulation Results

Algorithm makes use of currents to minimize expected energy usage
Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax

Simulation Results

Communication constraints with and without spatial deconfliction
Communication break distance 50m and 80m

Conclusions

Recent improvements of the planner include currents and communication constraints
Thereby enhances usability for mission planning
Barrier function approach allows for “probing” the path limits (useful for obstacle avoidance)
Algorithm easily adaptable for arbitrary number of vehicles

Future Work

Running time increases exponentially with number of discrete points  use different optimization approach and/or different means of path description
Incorporate real vehicle dynamics instead of approximation through constraints
Improve communication constraint
Use more sophisticated energy usage equation
Allow for specification of vehicle sub-groups